Properties

Label 138.2.e.b.55.1
Level $138$
Weight $2$
Character 138.55
Analytic conductor $1.102$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [138,2,Mod(13,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 138.e (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.10193554789\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 55.1
Root \(0.959493 - 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 138.55
Dual form 138.2.e.b.133.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.544078 - 3.78415i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.20217 - 2.63238i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.544078 - 3.78415i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.20217 - 2.63238i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.58816 + 3.47758i) q^{10} +(1.51662 + 0.445319i) q^{11} +(0.959493 + 0.281733i) q^{12} +(1.95653 + 4.28419i) q^{13} +(-0.411844 + 2.86444i) q^{14} +(2.50357 - 2.88927i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-3.98569 - 2.56145i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.80728 - 1.16147i) q^{19} +(-2.50357 - 2.88927i) q^{20} +(2.77667 - 0.815304i) q^{21} -1.58065 q^{22} +(2.88909 + 3.82794i) q^{23} -1.00000 q^{24} +(-9.22627 + 2.70908i) q^{25} +(-3.08427 - 3.55944i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.411844 - 2.86444i) q^{28} +(-0.495008 - 0.318122i) q^{29} +(-1.58816 + 3.47758i) q^{30} +(-0.111819 + 0.129046i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.656624 + 1.43781i) q^{33} +(4.54589 + 1.33479i) q^{34} +(-10.6154 - 3.11696i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.685789 + 4.76977i) q^{37} +(-1.40685 + 1.62359i) q^{38} +(-1.95653 + 4.28419i) q^{39} +(3.21616 + 2.06690i) q^{40} +(1.47968 + 10.2914i) q^{41} +(-2.43450 + 1.56456i) q^{42} +(-8.03389 - 9.27160i) q^{43} +(1.51662 - 0.445319i) q^{44} +3.82306 q^{45} +(-3.85052 - 2.85894i) q^{46} +5.45520 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.900187 - 1.03887i) q^{49} +(8.08931 - 5.19868i) q^{50} +(-0.674259 - 4.68958i) q^{51} +(3.96215 + 2.54632i) q^{52} +(-4.28201 + 9.37628i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.859995 - 5.98139i) q^{55} +(1.20217 + 2.63238i) q^{56} +(2.06130 + 0.605253i) q^{57} +(0.564582 + 0.165776i) q^{58} +(-0.790420 - 1.73078i) q^{59} +(0.544078 - 3.78415i) q^{60} +(8.28691 - 9.56361i) q^{61} +(0.0709331 - 0.155322i) q^{62} +(2.43450 + 1.56456i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(15.1475 - 9.73472i) q^{65} +(-1.03510 - 1.19457i) q^{66} +(-5.63806 + 1.65548i) q^{67} -4.73780 q^{68} +(-1.00102 + 4.69020i) q^{69} +11.0635 q^{70} +(11.3427 - 3.33053i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-11.1159 + 7.14378i) q^{73} +(-0.685789 - 4.76977i) q^{74} +(-8.08931 - 5.19868i) q^{75} +(0.892446 - 1.95418i) q^{76} +(2.99548 - 3.45697i) q^{77} +(0.670276 - 4.66187i) q^{78} +(4.85393 + 10.6286i) q^{79} +(-3.66820 - 1.07708i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-4.31917 - 9.45767i) q^{82} +(0.0161168 - 0.112095i) q^{83} +(1.89510 - 2.18706i) q^{84} +(-7.52436 + 16.4761i) q^{85} +(10.3206 + 6.63263i) q^{86} +(-0.0837405 - 0.582428i) q^{87} +(-1.32972 + 0.854562i) q^{88} +(8.01460 + 9.24934i) q^{89} +(-3.66820 + 1.07708i) q^{90} +13.6297 q^{91} +(4.50000 + 1.65831i) q^{92} -0.170752 q^{93} +(-5.23423 + 1.53691i) q^{94} +(-5.37848 - 6.20710i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-0.124317 - 0.864646i) q^{97} +(1.15641 + 0.743178i) q^{98} +(-0.656624 + 1.43781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.959493 + 0.281733i −0.678464 + 0.199215i
\(3\) 0.654861 + 0.755750i 0.378084 + 0.436332i
\(4\) 0.841254 0.540641i 0.420627 0.270320i
\(5\) −0.544078 3.78415i −0.243319 1.69232i −0.635234 0.772320i \(-0.719096\pi\)
0.391915 0.920001i \(-0.371813\pi\)
\(6\) −0.841254 0.540641i −0.343440 0.220716i
\(7\) 1.20217 2.63238i 0.454376 0.994946i −0.534357 0.845259i \(-0.679446\pi\)
0.988733 0.149687i \(-0.0478265\pi\)
\(8\) −0.654861 + 0.755750i −0.231528 + 0.267198i
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 1.58816 + 3.47758i 0.502219 + 1.09971i
\(11\) 1.51662 + 0.445319i 0.457278 + 0.134269i 0.502256 0.864719i \(-0.332504\pi\)
−0.0449780 + 0.998988i \(0.514322\pi\)
\(12\) 0.959493 + 0.281733i 0.276982 + 0.0813292i
\(13\) 1.95653 + 4.28419i 0.542643 + 1.18822i 0.960134 + 0.279541i \(0.0901822\pi\)
−0.417491 + 0.908681i \(0.637091\pi\)
\(14\) −0.411844 + 2.86444i −0.110070 + 0.765553i
\(15\) 2.50357 2.88927i 0.646419 0.746008i
\(16\) 0.415415 0.909632i 0.103854 0.227408i
\(17\) −3.98569 2.56145i −0.966672 0.621242i −0.0408352 0.999166i \(-0.513002\pi\)
−0.925837 + 0.377924i \(0.876638\pi\)
\(18\) −0.142315 0.989821i −0.0335439 0.233303i
\(19\) 1.80728 1.16147i 0.414619 0.266460i −0.316658 0.948540i \(-0.602561\pi\)
0.731278 + 0.682080i \(0.238924\pi\)
\(20\) −2.50357 2.88927i −0.559815 0.646062i
\(21\) 2.77667 0.815304i 0.605919 0.177914i
\(22\) −1.58065 −0.336995
\(23\) 2.88909 + 3.82794i 0.602417 + 0.798182i
\(24\) −1.00000 −0.204124
\(25\) −9.22627 + 2.70908i −1.84525 + 0.541815i
\(26\) −3.08427 3.55944i −0.604875 0.698063i
\(27\) −0.841254 + 0.540641i −0.161899 + 0.104046i
\(28\) −0.411844 2.86444i −0.0778312 0.541328i
\(29\) −0.495008 0.318122i −0.0919207 0.0590739i 0.493873 0.869534i \(-0.335581\pi\)
−0.585794 + 0.810460i \(0.699217\pi\)
\(30\) −1.58816 + 3.47758i −0.289956 + 0.634916i
\(31\) −0.111819 + 0.129046i −0.0200833 + 0.0231774i −0.765702 0.643195i \(-0.777608\pi\)
0.745619 + 0.666372i \(0.232154\pi\)
\(32\) −0.142315 + 0.989821i −0.0251579 + 0.174977i
\(33\) 0.656624 + 1.43781i 0.114304 + 0.250290i
\(34\) 4.54589 + 1.33479i 0.779613 + 0.228915i
\(35\) −10.6154 3.11696i −1.79433 0.526862i
\(36\) 0.415415 + 0.909632i 0.0692358 + 0.151605i
\(37\) −0.685789 + 4.76977i −0.112743 + 0.784145i 0.852488 + 0.522747i \(0.175093\pi\)
−0.965231 + 0.261398i \(0.915816\pi\)
\(38\) −1.40685 + 1.62359i −0.228222 + 0.263382i
\(39\) −1.95653 + 4.28419i −0.313295 + 0.686020i
\(40\) 3.21616 + 2.06690i 0.508520 + 0.326806i
\(41\) 1.47968 + 10.2914i 0.231088 + 1.60725i 0.693414 + 0.720540i \(0.256106\pi\)
−0.462326 + 0.886710i \(0.652985\pi\)
\(42\) −2.43450 + 1.56456i −0.375651 + 0.241416i
\(43\) −8.03389 9.27160i −1.22516 1.41391i −0.879739 0.475456i \(-0.842283\pi\)
−0.345417 0.938449i \(-0.612262\pi\)
\(44\) 1.51662 0.445319i 0.228639 0.0671344i
\(45\) 3.82306 0.569908
\(46\) −3.85052 2.85894i −0.567728 0.421527i
\(47\) 5.45520 0.795723 0.397862 0.917445i \(-0.369752\pi\)
0.397862 + 0.917445i \(0.369752\pi\)
\(48\) 0.959493 0.281733i 0.138491 0.0406646i
\(49\) −0.900187 1.03887i −0.128598 0.148410i
\(50\) 8.08931 5.19868i 1.14400 0.735205i
\(51\) −0.674259 4.68958i −0.0944152 0.656672i
\(52\) 3.96215 + 2.54632i 0.549451 + 0.353110i
\(53\) −4.28201 + 9.37628i −0.588179 + 1.28793i 0.348358 + 0.937362i \(0.386739\pi\)
−0.936537 + 0.350570i \(0.885988\pi\)
\(54\) 0.654861 0.755750i 0.0891153 0.102844i
\(55\) 0.859995 5.98139i 0.115962 0.806531i
\(56\) 1.20217 + 2.63238i 0.160646 + 0.351766i
\(57\) 2.06130 + 0.605253i 0.273026 + 0.0801677i
\(58\) 0.564582 + 0.165776i 0.0741333 + 0.0217675i
\(59\) −0.790420 1.73078i −0.102904 0.225328i 0.851176 0.524881i \(-0.175890\pi\)
−0.954080 + 0.299552i \(0.903163\pi\)
\(60\) 0.544078 3.78415i 0.0702402 0.488531i
\(61\) 8.28691 9.56361i 1.06103 1.22449i 0.0874457 0.996169i \(-0.472130\pi\)
0.973585 0.228325i \(-0.0733250\pi\)
\(62\) 0.0709331 0.155322i 0.00900851 0.0197259i
\(63\) 2.43450 + 1.56456i 0.306718 + 0.197116i
\(64\) −0.142315 0.989821i −0.0177894 0.123728i
\(65\) 15.1475 9.73472i 1.87882 1.20744i
\(66\) −1.03510 1.19457i −0.127412 0.147042i
\(67\) −5.63806 + 1.65548i −0.688799 + 0.202250i −0.607358 0.794429i \(-0.707770\pi\)
−0.0814412 + 0.996678i \(0.525952\pi\)
\(68\) −4.73780 −0.574543
\(69\) −1.00102 + 4.69020i −0.120508 + 0.564634i
\(70\) 11.0635 1.32234
\(71\) 11.3427 3.33053i 1.34614 0.395261i 0.472281 0.881448i \(-0.343431\pi\)
0.873855 + 0.486187i \(0.161612\pi\)
\(72\) −0.654861 0.755750i −0.0771761 0.0890659i
\(73\) −11.1159 + 7.14378i −1.30102 + 0.836116i −0.993323 0.115368i \(-0.963195\pi\)
−0.307699 + 0.951484i \(0.599559\pi\)
\(74\) −0.685789 4.76977i −0.0797213 0.554474i
\(75\) −8.08931 5.19868i −0.934073 0.600292i
\(76\) 0.892446 1.95418i 0.102371 0.224160i
\(77\) 2.99548 3.45697i 0.341366 0.393958i
\(78\) 0.670276 4.66187i 0.0758938 0.527853i
\(79\) 4.85393 + 10.6286i 0.546110 + 1.19581i 0.958575 + 0.284841i \(0.0919408\pi\)
−0.412465 + 0.910974i \(0.635332\pi\)
\(80\) −3.66820 1.07708i −0.410117 0.120421i
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) −4.31917 9.45767i −0.476973 1.04442i
\(83\) 0.0161168 0.112095i 0.00176905 0.0123040i −0.988918 0.148464i \(-0.952567\pi\)
0.990687 + 0.136160i \(0.0434761\pi\)
\(84\) 1.89510 2.18706i 0.206772 0.238628i
\(85\) −7.52436 + 16.4761i −0.816132 + 1.78708i
\(86\) 10.3206 + 6.63263i 1.11290 + 0.715214i
\(87\) −0.0837405 0.582428i −0.00897793 0.0624429i
\(88\) −1.32972 + 0.854562i −0.141749 + 0.0910966i
\(89\) 8.01460 + 9.24934i 0.849546 + 0.980428i 0.999966 0.00819403i \(-0.00260827\pi\)
−0.150421 + 0.988622i \(0.548063\pi\)
\(90\) −3.66820 + 1.07708i −0.386662 + 0.113534i
\(91\) 13.6297 1.42878
\(92\) 4.50000 + 1.65831i 0.469157 + 0.172891i
\(93\) −0.170752 −0.0177062
\(94\) −5.23423 + 1.53691i −0.539869 + 0.158520i
\(95\) −5.37848 6.20710i −0.551820 0.636835i
\(96\) −0.841254 + 0.540641i −0.0858601 + 0.0551789i
\(97\) −0.124317 0.864646i −0.0126225 0.0877915i 0.982536 0.186071i \(-0.0595753\pi\)
−0.995159 + 0.0982791i \(0.968666\pi\)
\(98\) 1.15641 + 0.743178i 0.116815 + 0.0750723i
\(99\) −0.656624 + 1.43781i −0.0659932 + 0.144505i
\(100\) −6.29699 + 7.26712i −0.629699 + 0.726712i
\(101\) 1.55270 10.7992i 0.154499 1.07456i −0.754060 0.656806i \(-0.771907\pi\)
0.908558 0.417758i \(-0.137184\pi\)
\(102\) 1.96815 + 4.30965i 0.194876 + 0.426719i
\(103\) −3.54321 1.04038i −0.349123 0.102512i 0.102469 0.994736i \(-0.467326\pi\)
−0.451592 + 0.892224i \(0.649144\pi\)
\(104\) −4.51903 1.32691i −0.443127 0.130114i
\(105\) −4.59596 10.0637i −0.448519 0.982120i
\(106\) 1.46695 10.2029i 0.142483 0.990989i
\(107\) −7.05053 + 8.13674i −0.681600 + 0.786608i −0.986144 0.165890i \(-0.946950\pi\)
0.304544 + 0.952498i \(0.401496\pi\)
\(108\) −0.415415 + 0.909632i −0.0399733 + 0.0875294i
\(109\) −6.99382 4.49466i −0.669887 0.430510i 0.160998 0.986955i \(-0.448529\pi\)
−0.830885 + 0.556445i \(0.812165\pi\)
\(110\) 0.859995 + 5.98139i 0.0819973 + 0.570304i
\(111\) −4.05384 + 2.60525i −0.384774 + 0.247279i
\(112\) −1.89510 2.18706i −0.179070 0.206658i
\(113\) −7.20846 + 2.11660i −0.678115 + 0.199113i −0.602614 0.798033i \(-0.705874\pi\)
−0.0755016 + 0.997146i \(0.524056\pi\)
\(114\) −2.14832 −0.201209
\(115\) 12.9136 13.0154i 1.20420 1.21370i
\(116\) −0.588417 −0.0546332
\(117\) −4.51903 + 1.32691i −0.417785 + 0.122673i
\(118\) 1.24602 + 1.43798i 0.114705 + 0.132377i
\(119\) −11.5342 + 7.41256i −1.05734 + 0.679508i
\(120\) 0.544078 + 3.78415i 0.0496673 + 0.345444i
\(121\) −7.15197 4.59629i −0.650179 0.417844i
\(122\) −5.25686 + 11.5109i −0.475933 + 1.04215i
\(123\) −6.80875 + 7.85772i −0.613924 + 0.708506i
\(124\) −0.0243006 + 0.169014i −0.00218226 + 0.0151779i
\(125\) 7.33057 + 16.0517i 0.655666 + 1.43571i
\(126\) −2.77667 0.815304i −0.247366 0.0726331i
\(127\) 7.28023 + 2.13767i 0.646016 + 0.189687i 0.588296 0.808645i \(-0.299799\pi\)
0.0577198 + 0.998333i \(0.481617\pi\)
\(128\) 0.415415 + 0.909632i 0.0367178 + 0.0804009i
\(129\) 1.74593 12.1432i 0.153721 1.06915i
\(130\) −11.7913 + 13.6079i −1.03417 + 1.19350i
\(131\) 7.39794 16.1992i 0.646361 1.41533i −0.248343 0.968672i \(-0.579886\pi\)
0.894704 0.446660i \(-0.147387\pi\)
\(132\) 1.32972 + 0.854562i 0.115738 + 0.0743801i
\(133\) −0.884774 6.15374i −0.0767196 0.533597i
\(134\) 4.94328 3.17685i 0.427034 0.274438i
\(135\) 2.50357 + 2.88927i 0.215473 + 0.248669i
\(136\) 4.54589 1.33479i 0.389806 0.114458i
\(137\) −0.762968 −0.0651847 −0.0325924 0.999469i \(-0.510376\pi\)
−0.0325924 + 0.999469i \(0.510376\pi\)
\(138\) −0.360914 4.78223i −0.0307230 0.407091i
\(139\) 9.22612 0.782549 0.391275 0.920274i \(-0.372034\pi\)
0.391275 + 0.920274i \(0.372034\pi\)
\(140\) −10.6154 + 3.11696i −0.897163 + 0.263431i
\(141\) 3.57240 + 4.12277i 0.300850 + 0.347200i
\(142\) −9.94497 + 6.39124i −0.834563 + 0.536341i
\(143\) 1.05947 + 7.36877i 0.0885973 + 0.616207i
\(144\) 0.841254 + 0.540641i 0.0701045 + 0.0450534i
\(145\) −0.934499 + 2.04627i −0.0776059 + 0.169933i
\(146\) 8.65303 9.98613i 0.716130 0.826458i
\(147\) 0.195629 1.36063i 0.0161352 0.112223i
\(148\) 2.00181 + 4.38335i 0.164548 + 0.360309i
\(149\) −17.7421 5.20954i −1.45349 0.426782i −0.542794 0.839866i \(-0.682633\pi\)
−0.910693 + 0.413084i \(0.864452\pi\)
\(150\) 9.22627 + 2.70908i 0.753322 + 0.221195i
\(151\) −0.412045 0.902252i −0.0335317 0.0734243i 0.892125 0.451789i \(-0.149214\pi\)
−0.925657 + 0.378364i \(0.876487\pi\)
\(152\) −0.305738 + 2.12646i −0.0247986 + 0.172478i
\(153\) 3.10260 3.58059i 0.250830 0.289474i
\(154\) −1.90020 + 4.16086i −0.153123 + 0.335292i
\(155\) 0.549167 + 0.352928i 0.0441102 + 0.0283479i
\(156\) 0.670276 + 4.66187i 0.0536650 + 0.373248i
\(157\) 6.82233 4.38445i 0.544481 0.349917i −0.239308 0.970944i \(-0.576921\pi\)
0.783789 + 0.621027i \(0.213284\pi\)
\(158\) −7.65175 8.83059i −0.608740 0.702524i
\(159\) −9.89024 + 2.90404i −0.784347 + 0.230305i
\(160\) 3.82306 0.302239
\(161\) 13.5498 3.00335i 1.06787 0.236697i
\(162\) 1.00000 0.0785674
\(163\) 22.1412 6.50124i 1.73423 0.509217i 0.746502 0.665383i \(-0.231732\pi\)
0.987731 + 0.156166i \(0.0499135\pi\)
\(164\) 6.80875 + 7.85772i 0.531674 + 0.613585i
\(165\) 5.08361 3.26704i 0.395759 0.254339i
\(166\) 0.0161168 + 0.112095i 0.00125091 + 0.00870026i
\(167\) −4.44588 2.85719i −0.344032 0.221096i 0.357202 0.934027i \(-0.383731\pi\)
−0.701234 + 0.712931i \(0.747367\pi\)
\(168\) −1.20217 + 2.63238i −0.0927492 + 0.203092i
\(169\) −6.01314 + 6.93953i −0.462549 + 0.533810i
\(170\) 2.57773 17.9285i 0.197703 1.37505i
\(171\) 0.892446 + 1.95418i 0.0682470 + 0.149440i
\(172\) −11.7711 3.45632i −0.897541 0.263542i
\(173\) −13.8077 4.05430i −1.04978 0.308243i −0.289051 0.957314i \(-0.593340\pi\)
−0.760728 + 0.649071i \(0.775158\pi\)
\(174\) 0.244437 + 0.535243i 0.0185308 + 0.0405767i
\(175\) −3.96020 + 27.5438i −0.299363 + 2.08212i
\(176\) 1.03510 1.19457i 0.0780238 0.0900443i
\(177\) 0.790420 1.73078i 0.0594116 0.130093i
\(178\) −10.2958 6.61670i −0.771702 0.495943i
\(179\) −1.59394 11.0861i −0.119136 0.828612i −0.958510 0.285057i \(-0.907987\pi\)
0.839374 0.543554i \(-0.182922\pi\)
\(180\) 3.21616 2.06690i 0.239719 0.154058i
\(181\) −5.75929 6.64657i −0.428084 0.494036i 0.500198 0.865911i \(-0.333260\pi\)
−0.928283 + 0.371875i \(0.878715\pi\)
\(182\) −13.0776 + 3.83993i −0.969376 + 0.284634i
\(183\) 12.6545 0.935445
\(184\) −4.78492 0.323343i −0.352749 0.0238371i
\(185\) 18.4226 1.35446
\(186\) 0.163836 0.0481065i 0.0120130 0.00352734i
\(187\) −4.90411 5.65965i −0.358624 0.413874i
\(188\) 4.58921 2.94931i 0.334702 0.215100i
\(189\) 0.411844 + 2.86444i 0.0299572 + 0.208357i
\(190\) 6.90935 + 4.44037i 0.501257 + 0.322138i
\(191\) −2.63041 + 5.75979i −0.190330 + 0.416764i −0.980607 0.195986i \(-0.937209\pi\)
0.790277 + 0.612750i \(0.209937\pi\)
\(192\) 0.654861 0.755750i 0.0472605 0.0545415i
\(193\) 0.437455 3.04256i 0.0314887 0.219009i −0.968001 0.250946i \(-0.919258\pi\)
0.999490 + 0.0319370i \(0.0101676\pi\)
\(194\) 0.362880 + 0.794597i 0.0260533 + 0.0570488i
\(195\) 17.2765 + 5.07284i 1.23720 + 0.363274i
\(196\) −1.31894 0.387276i −0.0942101 0.0276626i
\(197\) −0.400217 0.876353i −0.0285143 0.0624376i 0.894839 0.446389i \(-0.147290\pi\)
−0.923353 + 0.383951i \(0.874563\pi\)
\(198\) 0.224949 1.56456i 0.0159865 0.111188i
\(199\) −2.14354 + 2.47378i −0.151952 + 0.175362i −0.826622 0.562758i \(-0.809740\pi\)
0.674670 + 0.738119i \(0.264286\pi\)
\(200\) 3.99454 8.74682i 0.282456 0.618493i
\(201\) −4.94328 3.17685i −0.348672 0.224078i
\(202\) 1.55270 + 10.7992i 0.109247 + 0.759831i
\(203\) −1.43250 + 0.920613i −0.100542 + 0.0646144i
\(204\) −3.10260 3.58059i −0.217225 0.250691i
\(205\) 38.1392 11.1987i 2.66375 0.782149i
\(206\) 3.69279 0.257289
\(207\) −4.20014 + 2.31491i −0.291930 + 0.160897i
\(208\) 4.70981 0.326567
\(209\) 3.25819 0.956690i 0.225373 0.0661756i
\(210\) 7.24507 + 8.36126i 0.499957 + 0.576981i
\(211\) −20.5413 + 13.2011i −1.41412 + 0.908798i −0.999999 0.00142429i \(-0.999547\pi\)
−0.414119 + 0.910223i \(0.635910\pi\)
\(212\) 1.46695 + 10.2029i 0.100751 + 0.700735i
\(213\) 9.94497 + 6.39124i 0.681418 + 0.437921i
\(214\) 4.47255 9.79351i 0.305737 0.669470i
\(215\) −30.7140 + 35.4459i −2.09468 + 2.41739i
\(216\) 0.142315 0.989821i 0.00968330 0.0673488i
\(217\) 0.205273 + 0.449485i 0.0139348 + 0.0305130i
\(218\) 7.97681 + 2.34220i 0.540258 + 0.158634i
\(219\) −12.6783 3.72268i −0.856720 0.251556i
\(220\) −2.51031 5.49682i −0.169245 0.370595i
\(221\) 3.17563 22.0870i 0.213616 1.48573i
\(222\) 3.15565 3.64182i 0.211793 0.244423i
\(223\) 6.31394 13.8256i 0.422813 0.925831i −0.571626 0.820514i \(-0.693687\pi\)
0.994439 0.105316i \(-0.0335856\pi\)
\(224\) 2.43450 + 1.56456i 0.162662 + 0.104536i
\(225\) −1.36847 9.51790i −0.0912312 0.634527i
\(226\) 6.32016 4.06172i 0.420411 0.270181i
\(227\) −8.46896 9.77370i −0.562105 0.648703i 0.401555 0.915835i \(-0.368470\pi\)
−0.963660 + 0.267131i \(0.913924\pi\)
\(228\) 2.06130 0.605253i 0.136513 0.0400838i
\(229\) −0.948502 −0.0626788 −0.0313394 0.999509i \(-0.509977\pi\)
−0.0313394 + 0.999509i \(0.509977\pi\)
\(230\) −8.72365 + 16.1264i −0.575220 + 1.06334i
\(231\) 4.57422 0.300962
\(232\) 0.564582 0.165776i 0.0370667 0.0108838i
\(233\) −9.13414 10.5414i −0.598397 0.690587i 0.373058 0.927808i \(-0.378309\pi\)
−0.971456 + 0.237220i \(0.923764\pi\)
\(234\) 3.96215 2.54632i 0.259014 0.166458i
\(235\) −2.96806 20.6433i −0.193615 1.34662i
\(236\) −1.60067 1.02869i −0.104195 0.0669621i
\(237\) −4.85393 + 10.6286i −0.315297 + 0.690404i
\(238\) 8.97859 10.3618i 0.581996 0.671659i
\(239\) 0.347717 2.41842i 0.0224919 0.156435i −0.975480 0.220087i \(-0.929366\pi\)
0.997972 + 0.0636524i \(0.0202749\pi\)
\(240\) −1.58816 3.47758i −0.102515 0.224477i
\(241\) −10.4235 3.06062i −0.671438 0.197152i −0.0717947 0.997419i \(-0.522873\pi\)
−0.599643 + 0.800267i \(0.704691\pi\)
\(242\) 8.15719 + 2.39517i 0.524364 + 0.153967i
\(243\) −0.415415 0.909632i −0.0266489 0.0583529i
\(244\) 1.80092 12.5257i 0.115292 0.801873i
\(245\) −3.44147 + 3.97166i −0.219867 + 0.253740i
\(246\) 4.31917 9.45767i 0.275380 0.602999i
\(247\) 8.51197 + 5.47031i 0.541603 + 0.348067i
\(248\) −0.0243006 0.169014i −0.00154309 0.0107324i
\(249\) 0.0952700 0.0612263i 0.00603749 0.00388006i
\(250\) −11.5559 13.3362i −0.730861 0.843458i
\(251\) 13.7410 4.03472i 0.867324 0.254669i 0.182347 0.983234i \(-0.441630\pi\)
0.684977 + 0.728565i \(0.259812\pi\)
\(252\) 2.89389 0.182298
\(253\) 2.67699 + 7.09210i 0.168301 + 0.445877i
\(254\) −7.58758 −0.476087
\(255\) −17.3792 + 5.10299i −1.08833 + 0.319562i
\(256\) −0.654861 0.755750i −0.0409288 0.0472343i
\(257\) −3.57053 + 2.29464i −0.222724 + 0.143136i −0.647245 0.762282i \(-0.724079\pi\)
0.424521 + 0.905418i \(0.360442\pi\)
\(258\) 1.74593 + 12.1432i 0.108697 + 0.756003i
\(259\) 11.7314 + 7.53931i 0.728953 + 0.468470i
\(260\) 7.47991 16.3787i 0.463885 1.01577i
\(261\) 0.385331 0.444696i 0.0238514 0.0275260i
\(262\) −2.53442 + 17.6273i −0.156577 + 1.08902i
\(263\) −2.95101 6.46180i −0.181967 0.398452i 0.796563 0.604555i \(-0.206649\pi\)
−0.978530 + 0.206103i \(0.933922\pi\)
\(264\) −1.51662 0.445319i −0.0933414 0.0274075i
\(265\) 37.8110 + 11.1023i 2.32271 + 0.682009i
\(266\) 2.58264 + 5.65520i 0.158352 + 0.346743i
\(267\) −1.74174 + 12.1141i −0.106593 + 0.741368i
\(268\) −3.84802 + 4.44085i −0.235055 + 0.271268i
\(269\) −3.21213 + 7.03359i −0.195847 + 0.428846i −0.981922 0.189286i \(-0.939383\pi\)
0.786075 + 0.618131i \(0.212110\pi\)
\(270\) −3.21616 2.06690i −0.195729 0.125788i
\(271\) 0.723042 + 5.02887i 0.0439217 + 0.305482i 0.999926 + 0.0121307i \(0.00386142\pi\)
−0.956005 + 0.293351i \(0.905229\pi\)
\(272\) −3.98569 + 2.56145i −0.241668 + 0.155311i
\(273\) 8.92555 + 10.3006i 0.540199 + 0.623423i
\(274\) 0.732062 0.214953i 0.0442255 0.0129858i
\(275\) −15.1991 −0.916543
\(276\) 1.69360 + 4.48684i 0.101943 + 0.270076i
\(277\) −15.3909 −0.924751 −0.462376 0.886684i \(-0.653003\pi\)
−0.462376 + 0.886684i \(0.653003\pi\)
\(278\) −8.85240 + 2.59930i −0.530932 + 0.155896i
\(279\) −0.111819 0.129046i −0.00669443 0.00772578i
\(280\) 9.30723 5.98139i 0.556213 0.357457i
\(281\) 0.469579 + 3.26599i 0.0280127 + 0.194833i 0.999022 0.0442076i \(-0.0140763\pi\)
−0.971010 + 0.239040i \(0.923167\pi\)
\(282\) −4.58921 2.94931i −0.273283 0.175629i
\(283\) −10.7520 + 23.5436i −0.639141 + 1.39952i 0.261603 + 0.965175i \(0.415749\pi\)
−0.900745 + 0.434349i \(0.856979\pi\)
\(284\) 7.74150 8.93417i 0.459374 0.530146i
\(285\) 1.16886 8.12957i 0.0692370 0.481554i
\(286\) −3.09258 6.77180i −0.182868 0.400425i
\(287\) 28.8697 + 8.47692i 1.70413 + 0.500377i
\(288\) −0.959493 0.281733i −0.0565387 0.0166013i
\(289\) 2.26266 + 4.95453i 0.133098 + 0.291443i
\(290\) 0.320145 2.22666i 0.0187996 0.130754i
\(291\) 0.572045 0.660175i 0.0335339 0.0387002i
\(292\) −5.48910 + 12.0195i −0.321225 + 0.703386i
\(293\) 5.48975 + 3.52805i 0.320715 + 0.206111i 0.691085 0.722773i \(-0.257133\pi\)
−0.370371 + 0.928884i \(0.620769\pi\)
\(294\) 0.195629 + 1.36063i 0.0114093 + 0.0793537i
\(295\) −6.11947 + 3.93275i −0.356289 + 0.228973i
\(296\) −3.15565 3.64182i −0.183419 0.211676i
\(297\) −1.51662 + 0.445319i −0.0880031 + 0.0258401i
\(298\) 18.4911 1.07116
\(299\) −10.7471 + 19.8669i −0.621520 + 1.14893i
\(300\) −9.61578 −0.555167
\(301\) −34.0644 + 10.0022i −1.96344 + 0.576518i
\(302\) 0.649548 + 0.749618i 0.0373773 + 0.0431357i
\(303\) 9.17831 5.89854i 0.527280 0.338863i
\(304\) −0.305738 2.12646i −0.0175353 0.121961i
\(305\) −40.6988 26.1555i −2.33041 1.49766i
\(306\) −1.96815 + 4.30965i −0.112512 + 0.246367i
\(307\) −3.02366 + 3.48950i −0.172570 + 0.199156i −0.835445 0.549573i \(-0.814790\pi\)
0.662876 + 0.748729i \(0.269336\pi\)
\(308\) 0.650980 4.52766i 0.0370930 0.257988i
\(309\) −1.53404 3.35908i −0.0872686 0.191091i
\(310\) −0.626353 0.183914i −0.0355745 0.0104456i
\(311\) 10.3050 + 3.02582i 0.584342 + 0.171578i 0.560524 0.828138i \(-0.310600\pi\)
0.0238177 + 0.999716i \(0.492418\pi\)
\(312\) −1.95653 4.28419i −0.110766 0.242545i
\(313\) −3.79837 + 26.4182i −0.214696 + 1.49325i 0.542498 + 0.840057i \(0.317479\pi\)
−0.757194 + 0.653190i \(0.773430\pi\)
\(314\) −5.31074 + 6.12892i −0.299702 + 0.345875i
\(315\) 4.59596 10.0637i 0.258953 0.567027i
\(316\) 9.82966 + 6.31714i 0.552962 + 0.355367i
\(317\) −2.72980 18.9862i −0.153321 1.06637i −0.910603 0.413282i \(-0.864382\pi\)
0.757282 0.653087i \(-0.226527\pi\)
\(318\) 8.67145 5.57281i 0.486271 0.312507i
\(319\) −0.609073 0.702907i −0.0341015 0.0393553i
\(320\) −3.66820 + 1.07708i −0.205058 + 0.0602106i
\(321\) −10.7665 −0.600925
\(322\) −12.1548 + 6.69910i −0.677359 + 0.373326i
\(323\) −10.1783 −0.566337
\(324\) −0.959493 + 0.281733i −0.0533052 + 0.0156518i
\(325\) −29.6577 34.2268i −1.64511 1.89856i
\(326\) −19.4127 + 12.4758i −1.07517 + 0.690970i
\(327\) −1.18314 8.22895i −0.0654280 0.455062i
\(328\) −8.74672 5.62118i −0.482957 0.310378i
\(329\) 6.55807 14.3602i 0.361558 0.791701i
\(330\) −3.95726 + 4.56692i −0.217840 + 0.251401i
\(331\) −1.24393 + 8.65169i −0.0683723 + 0.475540i 0.926653 + 0.375918i \(0.122672\pi\)
−0.995025 + 0.0996221i \(0.968237\pi\)
\(332\) −0.0470448 0.103014i −0.00258192 0.00565361i
\(333\) −4.62362 1.35762i −0.253373 0.0743969i
\(334\) 5.07075 + 1.48891i 0.277459 + 0.0814694i
\(335\) 9.33214 + 20.4345i 0.509869 + 1.11646i
\(336\) 0.411844 2.86444i 0.0224679 0.156268i
\(337\) 2.13088 2.45916i 0.116076 0.133959i −0.694738 0.719263i \(-0.744479\pi\)
0.810814 + 0.585304i \(0.199025\pi\)
\(338\) 3.81447 8.35253i 0.207480 0.454318i
\(339\) −6.32016 4.06172i −0.343264 0.220602i
\(340\) 2.57773 + 17.9285i 0.139797 + 0.972311i
\(341\) −0.227054 + 0.145918i −0.0122956 + 0.00790193i
\(342\) −1.40685 1.62359i −0.0760739 0.0877939i
\(343\) 15.6198 4.58639i 0.843391 0.247642i
\(344\) 12.2681 0.661451
\(345\) 18.2930 + 1.23616i 0.984863 + 0.0665525i
\(346\) 14.3906 0.773644
\(347\) 5.00067 1.46833i 0.268450 0.0788241i −0.144737 0.989470i \(-0.546234\pi\)
0.413187 + 0.910646i \(0.364415\pi\)
\(348\) −0.385331 0.444696i −0.0206559 0.0238382i
\(349\) 13.0168 8.36539i 0.696773 0.447789i −0.143715 0.989619i \(-0.545905\pi\)
0.840488 + 0.541830i \(0.182268\pi\)
\(350\) −3.96020 27.5438i −0.211682 1.47228i
\(351\) −3.96215 2.54632i −0.211484 0.135912i
\(352\) −0.656624 + 1.43781i −0.0349982 + 0.0766353i
\(353\) 1.05867 1.22177i 0.0563473 0.0650283i −0.726876 0.686769i \(-0.759029\pi\)
0.783224 + 0.621740i \(0.213574\pi\)
\(354\) −0.270786 + 1.88336i −0.0143921 + 0.100099i
\(355\) −18.7746 41.1105i −0.996450 2.18192i
\(356\) 11.7429 + 3.44802i 0.622371 + 0.182745i
\(357\) −13.1553 3.86275i −0.696253 0.204438i
\(358\) 4.65268 + 10.1879i 0.245902 + 0.538449i
\(359\) −1.92950 + 13.4199i −0.101835 + 0.708278i 0.873383 + 0.487033i \(0.161921\pi\)
−0.975218 + 0.221244i \(0.928988\pi\)
\(360\) −2.50357 + 2.88927i −0.131950 + 0.152278i
\(361\) −5.97562 + 13.0848i −0.314507 + 0.688673i
\(362\) 7.39855 + 4.75476i 0.388859 + 0.249905i
\(363\) −1.20990 8.41502i −0.0635032 0.441674i
\(364\) 11.4660 7.36877i 0.600983 0.386228i
\(365\) 33.0810 + 38.1775i 1.73154 + 1.99830i
\(366\) −12.1419 + 3.56518i −0.634666 + 0.186355i
\(367\) 16.2735 0.849467 0.424734 0.905318i \(-0.360368\pi\)
0.424734 + 0.905318i \(0.360368\pi\)
\(368\) 4.68219 1.03782i 0.244076 0.0541002i
\(369\) −10.3972 −0.541259
\(370\) −17.6764 + 5.19025i −0.918950 + 0.269828i
\(371\) 19.5342 + 22.5437i 1.01417 + 1.17041i
\(372\) −0.143646 + 0.0923157i −0.00744770 + 0.00478635i
\(373\) −0.992630 6.90390i −0.0513965 0.357470i −0.999249 0.0387597i \(-0.987659\pi\)
0.947852 0.318710i \(-0.103250\pi\)
\(374\) 6.29997 + 4.04874i 0.325763 + 0.209355i
\(375\) −7.33057 + 16.0517i −0.378549 + 0.828907i
\(376\) −3.57240 + 4.12277i −0.184232 + 0.212615i
\(377\) 0.394402 2.74313i 0.0203127 0.141278i
\(378\) −1.20217 2.63238i −0.0618328 0.135395i
\(379\) −15.8428 4.65185i −0.813788 0.238950i −0.151749 0.988419i \(-0.548490\pi\)
−0.662039 + 0.749470i \(0.730309\pi\)
\(380\) −7.88047 2.31392i −0.404260 0.118701i
\(381\) 3.15200 + 6.90191i 0.161482 + 0.353595i
\(382\) 0.901138 6.26755i 0.0461062 0.320676i
\(383\) 14.6610 16.9196i 0.749140 0.864553i −0.245345 0.969436i \(-0.578901\pi\)
0.994485 + 0.104883i \(0.0334467\pi\)
\(384\) −0.415415 + 0.909632i −0.0211991 + 0.0464195i
\(385\) −14.7114 9.45447i −0.749764 0.481844i
\(386\) 0.437455 + 3.04256i 0.0222659 + 0.154862i
\(387\) 10.3206 6.63263i 0.524624 0.337155i
\(388\) −0.572045 0.660175i −0.0290412 0.0335153i
\(389\) 7.23675 2.12490i 0.366918 0.107737i −0.0930757 0.995659i \(-0.529670\pi\)
0.459994 + 0.887922i \(0.347852\pi\)
\(390\) −18.0059 −0.911763
\(391\) −1.70994 22.6573i −0.0864752 1.14583i
\(392\) 1.37462 0.0694290
\(393\) 17.0872 5.01725i 0.861934 0.253087i
\(394\) 0.630903 + 0.728101i 0.0317844 + 0.0366812i
\(395\) 37.5794 24.1508i 1.89082 1.21516i
\(396\) 0.224949 + 1.56456i 0.0113041 + 0.0786220i
\(397\) 24.1929 + 15.5478i 1.21421 + 0.780323i 0.981358 0.192190i \(-0.0615589\pi\)
0.232849 + 0.972513i \(0.425195\pi\)
\(398\) 1.35977 2.97748i 0.0681592 0.149248i
\(399\) 4.07128 4.69851i 0.203819 0.235220i
\(400\) −1.36847 + 9.51790i −0.0684234 + 0.475895i
\(401\) 2.83133 + 6.19974i 0.141390 + 0.309600i 0.967058 0.254555i \(-0.0819291\pi\)
−0.825668 + 0.564156i \(0.809202\pi\)
\(402\) 5.63806 + 1.65548i 0.281201 + 0.0825680i
\(403\) −0.771635 0.226573i −0.0384379 0.0112864i
\(404\) −4.53230 9.92434i −0.225490 0.493755i
\(405\) −0.544078 + 3.78415i −0.0270355 + 0.188036i
\(406\) 1.11511 1.28690i 0.0553419 0.0638680i
\(407\) −3.16415 + 6.92852i −0.156841 + 0.343434i
\(408\) 3.98569 + 2.56145i 0.197321 + 0.126811i
\(409\) 3.95559 + 27.5118i 0.195592 + 1.36037i 0.816889 + 0.576794i \(0.195697\pi\)
−0.621298 + 0.783574i \(0.713394\pi\)
\(410\) −33.4392 + 21.4901i −1.65145 + 1.06132i
\(411\) −0.499638 0.576613i −0.0246453 0.0284422i
\(412\) −3.54321 + 1.04038i −0.174561 + 0.0512558i
\(413\) −5.50628 −0.270947
\(414\) 3.37782 3.40446i 0.166011 0.167320i
\(415\) −0.432953 −0.0212528
\(416\) −4.51903 + 1.32691i −0.221564 + 0.0650570i
\(417\) 6.04182 + 6.97264i 0.295869 + 0.341452i
\(418\) −2.85668 + 1.83587i −0.139725 + 0.0897956i
\(419\) 2.15488 + 14.9875i 0.105273 + 0.732189i 0.972268 + 0.233871i \(0.0751395\pi\)
−0.866995 + 0.498317i \(0.833951\pi\)
\(420\) −9.30723 5.98139i −0.454146 0.291862i
\(421\) 15.8458 34.6974i 0.772276 1.69105i 0.0507004 0.998714i \(-0.483855\pi\)
0.721576 0.692335i \(-0.243418\pi\)
\(422\) 15.9900 18.4535i 0.778382 0.898301i
\(423\) −0.776356 + 5.39968i −0.0377477 + 0.262541i
\(424\) −4.28201 9.37628i −0.207953 0.455353i
\(425\) 43.7122 + 12.8351i 2.12035 + 0.622592i
\(426\) −11.3427 3.33053i −0.549558 0.161365i
\(427\) −15.2128 33.3114i −0.736198 1.61205i
\(428\) −1.53223 + 10.6569i −0.0740629 + 0.515119i
\(429\) −4.87514 + 5.62621i −0.235374 + 0.271636i
\(430\) 19.4836 42.6632i 0.939584 2.05740i
\(431\) 8.59239 + 5.52199i 0.413881 + 0.265985i 0.730969 0.682411i \(-0.239069\pi\)
−0.317088 + 0.948396i \(0.602705\pi\)
\(432\) 0.142315 + 0.989821i 0.00684713 + 0.0476228i
\(433\) −8.26339 + 5.31056i −0.397113 + 0.255209i −0.723923 0.689881i \(-0.757663\pi\)
0.326810 + 0.945090i \(0.394026\pi\)
\(434\) −0.323592 0.373446i −0.0155329 0.0179260i
\(435\) −2.15843 + 0.633773i −0.103489 + 0.0303871i
\(436\) −8.31357 −0.398148
\(437\) 9.66745 + 3.56259i 0.462457 + 0.170422i
\(438\) 13.2135 0.631367
\(439\) 7.48022 2.19639i 0.357011 0.104828i −0.0983084 0.995156i \(-0.531343\pi\)
0.455320 + 0.890328i \(0.349525\pi\)
\(440\) 3.95726 + 4.56692i 0.188655 + 0.217719i
\(441\) 1.15641 0.743178i 0.0550670 0.0353894i
\(442\) 3.17563 + 22.0870i 0.151049 + 1.05057i
\(443\) −23.7409 15.2573i −1.12796 0.724898i −0.162829 0.986654i \(-0.552062\pi\)
−0.965134 + 0.261756i \(0.915698\pi\)
\(444\) −2.00181 + 4.38335i −0.0950016 + 0.208024i
\(445\) 30.6403 35.3608i 1.45249 1.67626i
\(446\) −2.16306 + 15.0444i −0.102424 + 0.712373i
\(447\) −7.68147 16.8201i −0.363321 0.795562i
\(448\) −2.77667 0.815304i −0.131185 0.0385195i
\(449\) 12.2407 + 3.59418i 0.577673 + 0.169620i 0.557501 0.830176i \(-0.311760\pi\)
0.0201722 + 0.999797i \(0.493579\pi\)
\(450\) 3.99454 + 8.74682i 0.188304 + 0.412329i
\(451\) −2.33885 + 16.2671i −0.110132 + 0.765987i
\(452\) −4.91983 + 5.67778i −0.231409 + 0.267060i
\(453\) 0.412045 0.902252i 0.0193596 0.0423915i
\(454\) 10.8795 + 6.99182i 0.510599 + 0.328142i
\(455\) −7.41562 51.5767i −0.347649 2.41796i
\(456\) −1.80728 + 1.16147i −0.0846338 + 0.0543909i
\(457\) −6.13629 7.08166i −0.287044 0.331266i 0.593854 0.804573i \(-0.297606\pi\)
−0.880898 + 0.473307i \(0.843060\pi\)
\(458\) 0.910081 0.267224i 0.0425253 0.0124865i
\(459\) 4.73780 0.221142
\(460\) 3.82694 17.9309i 0.178432 0.836033i
\(461\) −11.6569 −0.542916 −0.271458 0.962450i \(-0.587506\pi\)
−0.271458 + 0.962450i \(0.587506\pi\)
\(462\) −4.38893 + 1.28871i −0.204192 + 0.0599561i
\(463\) −8.92436 10.2993i −0.414750 0.478647i 0.509480 0.860482i \(-0.329838\pi\)
−0.924230 + 0.381835i \(0.875292\pi\)
\(464\) −0.495008 + 0.318122i −0.0229802 + 0.0147685i
\(465\) 0.0929026 + 0.646152i 0.00430825 + 0.0299646i
\(466\) 11.7340 + 7.54097i 0.543566 + 0.349329i
\(467\) 2.73218 5.98265i 0.126430 0.276844i −0.835823 0.548999i \(-0.815009\pi\)
0.962253 + 0.272155i \(0.0877364\pi\)
\(468\) −3.08427 + 3.55944i −0.142570 + 0.164535i
\(469\) −2.42003 + 16.8317i −0.111747 + 0.777215i
\(470\) 8.66371 + 18.9709i 0.399627 + 0.875062i
\(471\) 7.78122 + 2.28477i 0.358540 + 0.105277i
\(472\) 1.82565 + 0.536060i 0.0840324 + 0.0246741i
\(473\) −8.05552 17.6391i −0.370393 0.811048i
\(474\) 1.66288 11.5656i 0.0763788 0.531226i
\(475\) −13.5280 + 15.6121i −0.620706 + 0.716333i
\(476\) −5.69563 + 12.4717i −0.261059 + 0.571639i
\(477\) −8.67145 5.57281i −0.397039 0.255161i
\(478\) 0.347717 + 2.41842i 0.0159042 + 0.110616i
\(479\) 7.77358 4.99577i 0.355184 0.228263i −0.350865 0.936426i \(-0.614112\pi\)
0.706049 + 0.708163i \(0.250476\pi\)
\(480\) 2.50357 + 2.88927i 0.114272 + 0.131877i
\(481\) −21.7764 + 6.39412i −0.992917 + 0.291547i
\(482\) 10.8636 0.494822
\(483\) 11.1430 + 8.27346i 0.507024 + 0.376455i
\(484\) −8.50156 −0.386434
\(485\) −3.20431 + 0.940870i −0.145500 + 0.0427227i
\(486\) 0.654861 + 0.755750i 0.0297051 + 0.0342815i
\(487\) −31.9883 + 20.5576i −1.44953 + 0.931556i −0.450277 + 0.892889i \(0.648675\pi\)
−0.999252 + 0.0386669i \(0.987689\pi\)
\(488\) 1.80092 + 12.5257i 0.0815237 + 0.567010i
\(489\) 19.4127 + 12.4758i 0.877873 + 0.564175i
\(490\) 2.18312 4.78036i 0.0986231 0.215955i
\(491\) 2.80715 3.23963i 0.126685 0.146202i −0.688863 0.724891i \(-0.741890\pi\)
0.815548 + 0.578689i \(0.196435\pi\)
\(492\) −1.47968 + 10.2914i −0.0667092 + 0.463973i
\(493\) 1.15810 + 2.53588i 0.0521580 + 0.114210i
\(494\) −9.70834 2.85062i −0.436799 0.128256i
\(495\) 5.79812 + 1.70248i 0.260606 + 0.0765209i
\(496\) 0.0709331 + 0.155322i 0.00318499 + 0.00697416i
\(497\) 4.86866 33.8623i 0.218389 1.51893i
\(498\) −0.0741615 + 0.0855869i −0.00332326 + 0.00383524i
\(499\) −12.5785 + 27.5431i −0.563091 + 1.23300i 0.387304 + 0.921952i \(0.373407\pi\)
−0.950395 + 0.311046i \(0.899321\pi\)
\(500\) 14.8451 + 9.54036i 0.663892 + 0.426658i
\(501\) −0.752109 5.23103i −0.0336018 0.233705i
\(502\) −12.0477 + 7.74258i −0.537714 + 0.345568i
\(503\) −7.63837 8.81514i −0.340578 0.393048i 0.559462 0.828856i \(-0.311008\pi\)
−0.900039 + 0.435808i \(0.856463\pi\)
\(504\) −2.77667 + 0.815304i −0.123683 + 0.0363165i
\(505\) −41.7107 −1.85610
\(506\) −4.56663 6.05063i −0.203011 0.268983i
\(507\) −9.18232 −0.407801
\(508\) 7.28023 2.13767i 0.323008 0.0948437i
\(509\) 10.0217 + 11.5656i 0.444203 + 0.512638i 0.933057 0.359728i \(-0.117130\pi\)
−0.488854 + 0.872366i \(0.662585\pi\)
\(510\) 15.2375 9.79257i 0.674729 0.433622i
\(511\) 5.44192 + 37.8494i 0.240736 + 1.67436i
\(512\) 0.841254 + 0.540641i 0.0371785 + 0.0238932i
\(513\) −0.892446 + 1.95418i −0.0394024 + 0.0862793i
\(514\) 2.77942 3.20763i 0.122595 0.141482i
\(515\) −2.00917 + 13.9741i −0.0885345 + 0.615771i
\(516\) −5.09635 11.1594i −0.224354 0.491267i
\(517\) 8.27346 + 2.42931i 0.363866 + 0.106841i
\(518\) −13.3803 3.92880i −0.587895 0.172622i
\(519\) −5.97807 13.0902i −0.262408 0.574594i
\(520\) −2.56250 + 17.8226i −0.112373 + 0.781573i
\(521\) −1.26434 + 1.45913i −0.0553918 + 0.0639256i −0.782769 0.622312i \(-0.786194\pi\)
0.727377 + 0.686238i \(0.240739\pi\)
\(522\) −0.244437 + 0.535243i −0.0106987 + 0.0234270i
\(523\) −15.3733 9.87985i −0.672229 0.432016i 0.159499 0.987198i \(-0.449012\pi\)
−0.831729 + 0.555183i \(0.812648\pi\)
\(524\) −2.53442 17.6273i −0.110717 0.770051i
\(525\) −23.4096 + 15.0444i −1.02168 + 0.656593i
\(526\) 4.65197 + 5.36866i 0.202836 + 0.234085i
\(527\) 0.776221 0.227919i 0.0338127 0.00992831i
\(528\) 1.58065 0.0687888
\(529\) −6.30632 + 22.1186i −0.274188 + 0.961676i
\(530\) −39.4072 −1.71174
\(531\) 1.82565 0.536060i 0.0792265 0.0232630i
\(532\) −4.07128 4.69851i −0.176512 0.203706i
\(533\) −41.1954 + 26.4747i −1.78437 + 1.14675i
\(534\) −1.74174 12.1141i −0.0753724 0.524227i
\(535\) 34.6266 + 22.2532i 1.49704 + 0.962089i
\(536\) 2.44101 5.34507i 0.105436 0.230872i
\(537\) 7.33448 8.46445i 0.316506 0.365268i
\(538\) 1.10043 7.65364i 0.0474428 0.329972i
\(539\) −0.902611 1.97644i −0.0388782 0.0851314i
\(540\) 3.66820 + 1.07708i 0.157854 + 0.0463501i
\(541\) −42.6494 12.5230i −1.83364 0.538405i −0.833734 0.552167i \(-0.813801\pi\)
−0.999905 + 0.0137620i \(0.995619\pi\)
\(542\) −2.11055 4.62146i −0.0906558 0.198509i
\(543\) 1.25161 8.70516i 0.0537118 0.373574i
\(544\) 3.10260 3.58059i 0.133023 0.153517i
\(545\) −13.2032 + 28.9111i −0.565565 + 1.23841i
\(546\) −11.4660 7.36877i −0.490701 0.315354i
\(547\) −2.71929 18.9131i −0.116268 0.808665i −0.961606 0.274433i \(-0.911510\pi\)
0.845338 0.534232i \(-0.179399\pi\)
\(548\) −0.641849 + 0.412491i −0.0274184 + 0.0176208i
\(549\) 8.28691 + 9.56361i 0.353677 + 0.408165i
\(550\) 14.5835 4.28209i 0.621841 0.182589i
\(551\) −1.26411 −0.0538529
\(552\) −2.88909 3.82794i −0.122968 0.162928i
\(553\) 33.8138 1.43791
\(554\) 14.7675 4.33613i 0.627411 0.184224i
\(555\) 12.0642 + 13.9229i 0.512099 + 0.590993i
\(556\) 7.76151 4.98802i 0.329161 0.211539i
\(557\) 6.27333 + 43.6320i 0.265809 + 1.84875i 0.486856 + 0.873482i \(0.338144\pi\)
−0.221047 + 0.975263i \(0.570947\pi\)
\(558\) 0.143646 + 0.0923157i 0.00608102 + 0.00390804i
\(559\) 24.0028 52.5589i 1.01521 2.22300i
\(560\) −7.24507 + 8.36126i −0.306160 + 0.353328i
\(561\) 1.06577 7.41256i 0.0449966 0.312958i
\(562\) −1.37069 3.00140i −0.0578192 0.126606i
\(563\) −37.8423 11.1115i −1.59486 0.468294i −0.640751 0.767749i \(-0.721377\pi\)
−0.954110 + 0.299455i \(0.903195\pi\)
\(564\) 5.23423 + 1.53691i 0.220401 + 0.0647155i
\(565\) 11.9315 + 26.1263i 0.501961 + 1.09914i
\(566\) 3.68348 25.6192i 0.154828 1.07685i
\(567\) −1.89510 + 2.18706i −0.0795866 + 0.0918479i
\(568\) −4.91087 + 10.7533i −0.206056 + 0.451199i
\(569\) −32.2425 20.7210i −1.35168 0.868669i −0.353897 0.935284i \(-0.615144\pi\)
−0.997779 + 0.0666150i \(0.978780\pi\)
\(570\) 1.16886 + 8.12957i 0.0489580 + 0.340510i
\(571\) −14.2767 + 9.17508i −0.597462 + 0.383965i −0.804137 0.594444i \(-0.797372\pi\)
0.206675 + 0.978410i \(0.433736\pi\)
\(572\) 4.87514 + 5.62621i 0.203840 + 0.235244i
\(573\) −6.07551 + 1.78393i −0.253808 + 0.0745248i
\(574\) −30.0885 −1.25587
\(575\) −37.0257 27.4909i −1.54408 1.14645i
\(576\) 1.00000 0.0416667
\(577\) 27.9974 8.22079i 1.16555 0.342236i 0.358962 0.933352i \(-0.383131\pi\)
0.806586 + 0.591116i \(0.201313\pi\)
\(578\) −3.56686 4.11638i −0.148362 0.171219i
\(579\) 2.58589 1.66185i 0.107466 0.0690641i
\(580\) 0.320145 + 2.22666i 0.0132933 + 0.0924569i
\(581\) −0.275701 0.177183i −0.0114380 0.00735077i
\(582\) −0.362880 + 0.794597i −0.0150419 + 0.0329371i
\(583\) −10.6696 + 12.3134i −0.441890 + 0.509968i
\(584\) 1.88048 13.0790i 0.0778149 0.541215i
\(585\) 7.47991 + 16.3787i 0.309256 + 0.677177i
\(586\) −6.26134 1.83850i −0.258654 0.0759476i
\(587\) 14.5667 + 4.27716i 0.601231 + 0.176537i 0.568163 0.822916i \(-0.307654\pi\)
0.0330675 + 0.999453i \(0.489472\pi\)
\(588\) −0.571039 1.25040i −0.0235493 0.0515657i
\(589\) −0.0522055 + 0.363097i −0.00215109 + 0.0149612i
\(590\) 4.76361 5.49750i 0.196115 0.226328i
\(591\) 0.400217 0.876353i 0.0164627 0.0360484i
\(592\) 4.05384 + 2.60525i 0.166612 + 0.107075i
\(593\) 4.44889 + 30.9427i 0.182694 + 1.27066i 0.850359 + 0.526203i \(0.176385\pi\)
−0.667665 + 0.744462i \(0.732706\pi\)
\(594\) 1.32972 0.854562i 0.0545592 0.0350631i
\(595\) 34.3257 + 39.6140i 1.40722 + 1.62401i
\(596\) −17.7421 + 5.20954i −0.726743 + 0.213391i
\(597\) −3.27328 −0.133967
\(598\) 4.71460 22.0899i 0.192794 0.903325i
\(599\) −30.8576 −1.26081 −0.630405 0.776267i \(-0.717111\pi\)
−0.630405 + 0.776267i \(0.717111\pi\)
\(600\) 9.22627 2.70908i 0.376661 0.110598i
\(601\) −4.34025 5.00891i −0.177042 0.204318i 0.660292 0.751009i \(-0.270433\pi\)
−0.837334 + 0.546691i \(0.815887\pi\)
\(602\) 29.8666 19.1941i 1.21727 0.782294i
\(603\) −0.836254 5.81627i −0.0340549 0.236857i
\(604\) −0.834429 0.536255i −0.0339524 0.0218199i
\(605\) −13.5018 + 29.5648i −0.548926 + 1.20198i
\(606\) −7.14472 + 8.24544i −0.290234 + 0.334948i
\(607\) 3.35546 23.3377i 0.136194 0.947250i −0.801055 0.598590i \(-0.795728\pi\)
0.937249 0.348660i \(-0.113363\pi\)
\(608\) 0.892446 + 1.95418i 0.0361934 + 0.0792526i
\(609\) −1.63384 0.479739i −0.0662066 0.0194400i
\(610\) 46.4191 + 13.6299i 1.87945 + 0.551857i
\(611\) 10.6732 + 23.3712i 0.431793 + 0.945496i
\(612\) 0.674259 4.68958i 0.0272553 0.189565i
\(613\) 21.3290 24.6150i 0.861469 0.994189i −0.138523 0.990359i \(-0.544236\pi\)
0.999993 0.00382949i \(-0.00121897\pi\)
\(614\) 1.91808 4.20001i 0.0774074 0.169499i
\(615\) 33.4392 + 21.4901i 1.34840 + 0.866564i
\(616\) 0.650980 + 4.52766i 0.0262287 + 0.182425i
\(617\) −5.04770 + 3.24396i −0.203213 + 0.130597i −0.638289 0.769797i \(-0.720358\pi\)
0.435077 + 0.900393i \(0.356721\pi\)
\(618\) 2.41826 + 2.79083i 0.0972769 + 0.112263i
\(619\) 12.3649 3.63066i 0.496986 0.145928i −0.0236271 0.999721i \(-0.507521\pi\)
0.520613 + 0.853792i \(0.325703\pi\)
\(620\) 0.652796 0.0262169
\(621\) −4.50000 1.65831i −0.180579 0.0665458i
\(622\) −10.7400 −0.430636
\(623\) 33.9827 9.97821i 1.36149 0.399768i
\(624\) 3.08427 + 3.55944i 0.123470 + 0.142492i
\(625\) 16.3071 10.4799i 0.652284 0.419197i
\(626\) −3.79837 26.4182i −0.151813 1.05588i
\(627\) 2.85668 + 1.83587i 0.114085 + 0.0733178i
\(628\) 3.36890 7.37686i 0.134434 0.294369i
\(629\) 14.9508 17.2542i 0.596129 0.687970i
\(630\) −1.57450 + 10.9509i −0.0627297 + 0.436295i
\(631\) 8.90725 + 19.5041i 0.354592 + 0.776448i 0.999921 + 0.0125435i \(0.00399282\pi\)
−0.645329 + 0.763904i \(0.723280\pi\)
\(632\) −11.2112 3.29192i −0.445959 0.130945i
\(633\) −23.4284 6.87919i −0.931193 0.273423i
\(634\) 7.96824 + 17.4480i 0.316459 + 0.692949i
\(635\) 4.12824 28.7125i 0.163824 1.13942i
\(636\) −6.75016 + 7.79010i −0.267661 + 0.308897i
\(637\) 2.68949 5.88915i 0.106561 0.233337i
\(638\) 0.782433 + 0.502839i 0.0309768 + 0.0199076i
\(639\) 1.68239 + 11.7013i 0.0665543 + 0.462895i
\(640\) 3.21616 2.06690i 0.127130 0.0817015i
\(641\) −20.1426 23.2459i −0.795587 0.918156i 0.202544 0.979273i \(-0.435079\pi\)
−0.998131 + 0.0611172i \(0.980534\pi\)
\(642\) 10.3303 3.03326i 0.407706 0.119713i
\(643\) 28.7980 1.13568 0.567842 0.823138i \(-0.307778\pi\)
0.567842 + 0.823138i \(0.307778\pi\)
\(644\) 9.77506 9.85214i 0.385191 0.388229i
\(645\) −46.9016 −1.84675
\(646\) 9.76603 2.86757i 0.384239 0.112823i
\(647\) 13.6600 + 15.7645i 0.537031 + 0.619767i 0.957812 0.287395i \(-0.0927893\pi\)
−0.420781 + 0.907162i \(0.638244\pi\)
\(648\) 0.841254 0.540641i 0.0330476 0.0212384i
\(649\) −0.428017 2.97692i −0.0168011 0.116854i
\(650\) 38.0991 + 24.4848i 1.49437 + 0.960373i
\(651\) −0.205273 + 0.449485i −0.00804528 + 0.0176167i
\(652\) 15.1115 17.4396i 0.591813 0.682989i
\(653\) −3.78327 + 26.3132i −0.148051 + 1.02972i 0.771355 + 0.636406i \(0.219580\pi\)
−0.919405 + 0.393311i \(0.871330\pi\)
\(654\) 3.45358 + 7.56229i 0.135046 + 0.295709i
\(655\) −65.3253 19.1812i −2.55247 0.749473i
\(656\) 9.97609 + 2.92924i 0.389501 + 0.114368i
\(657\) −5.48910 12.0195i −0.214150 0.468924i
\(658\) −2.24669 + 15.6261i −0.0875852 + 0.609169i
\(659\) 17.9541 20.7202i 0.699394 0.807144i −0.289276 0.957246i \(-0.593415\pi\)
0.988671 + 0.150102i \(0.0479601\pi\)
\(660\) 2.51031 5.49682i 0.0977138 0.213963i
\(661\) 6.84724 + 4.40046i 0.266327 + 0.171158i 0.666988 0.745068i \(-0.267583\pi\)
−0.400661 + 0.916226i \(0.631220\pi\)
\(662\) −1.24393 8.65169i −0.0483465 0.336257i
\(663\) 18.7718 12.0639i 0.729038 0.468524i
\(664\) 0.0741615 + 0.0855869i 0.00287802 + 0.00332142i
\(665\) −22.8053 + 6.69623i −0.884350 + 0.259669i
\(666\) 4.81881 0.186725
\(667\) −0.212368 2.81395i −0.00822292 0.108957i
\(668\) −5.28482 −0.204476
\(669\) 14.5834 4.28209i 0.563829 0.165555i
\(670\) −14.7112 16.9776i −0.568343 0.655903i
\(671\) 16.8269 10.8140i 0.649597 0.417471i
\(672\) 0.411844 + 2.86444i 0.0158872 + 0.110498i
\(673\) 26.0896 + 16.7667i 1.00568 + 0.646310i 0.936271 0.351278i \(-0.114253\pi\)
0.0694072 + 0.997588i \(0.477889\pi\)
\(674\) −1.35173 + 2.95989i −0.0520669 + 0.114011i
\(675\) 6.29699 7.26712i 0.242371 0.279712i
\(676\) −1.30678 + 9.08886i −0.0502608 + 0.349571i
\(677\) −8.47632 18.5606i −0.325772 0.713340i 0.673904 0.738819i \(-0.264616\pi\)
−0.999675 + 0.0254788i \(0.991889\pi\)
\(678\) 7.20846 + 2.11660i 0.276839 + 0.0812874i
\(679\) −2.42553 0.712199i −0.0930831 0.0273317i
\(680\) −7.52436 16.4761i −0.288546 0.631828i
\(681\) 1.84048 12.8008i 0.0705274 0.490529i
\(682\) 0.176746 0.203976i 0.00676797 0.00781065i
\(683\) 8.63468 18.9073i 0.330397 0.723468i −0.669414 0.742889i \(-0.733455\pi\)
0.999811 + 0.0194207i \(0.00618219\pi\)
\(684\) 1.80728 + 1.16147i 0.0691032 + 0.0444100i
\(685\) 0.415114 + 2.88718i 0.0158607 + 0.110314i
\(686\) −13.6950 + 8.80122i −0.522876 + 0.336032i
\(687\) −0.621137 0.716830i −0.0236978 0.0273488i
\(688\) −11.7711 + 3.45632i −0.448770 + 0.131771i
\(689\) −48.5477 −1.84952
\(690\) −17.9003 + 3.96766i −0.681453 + 0.151046i
\(691\) −13.6695 −0.520012 −0.260006 0.965607i \(-0.583725\pi\)
−0.260006 + 0.965607i \(0.583725\pi\)
\(692\) −13.8077 + 4.05430i −0.524890 + 0.154121i
\(693\) 2.99548 + 3.45697i 0.113789 + 0.131319i
\(694\) −4.38443 + 2.81770i −0.166431 + 0.106959i
\(695\) −5.01973 34.9130i −0.190409 1.32432i
\(696\) 0.495008 + 0.318122i 0.0187632 + 0.0120584i
\(697\) 20.4634 44.8085i 0.775106 1.69724i
\(698\) −10.1327 + 11.6938i −0.383529 + 0.442616i
\(699\) 1.98504 13.8062i 0.0750810 0.522200i
\(700\) 11.5598 + 25.3124i 0.436918 + 0.956718i
\(701\) 2.12031 + 0.622581i 0.0800832 + 0.0235145i 0.321529 0.946900i \(-0.395803\pi\)
−0.241446 + 0.970414i \(0.577622\pi\)
\(702\) 4.51903 + 1.32691i 0.170560 + 0.0500809i
\(703\) 4.30053 + 9.41685i 0.162198 + 0.355163i
\(704\) 0.224949 1.56456i 0.00847810 0.0589665i
\(705\) 13.6575 15.7616i 0.514371 0.593615i
\(706\) −0.671574 + 1.47054i −0.0252750 + 0.0553446i
\(707\) −26.5611 17.0698i −0.998932 0.641975i
\(708\) −0.270786 1.88336i −0.0101768 0.0707809i
\(709\) −15.7884 + 10.1466i −0.592946 + 0.381063i −0.802428 0.596749i \(-0.796459\pi\)
0.209482 + 0.977813i \(0.432822\pi\)
\(710\) 29.5962 + 34.1559i 1.11073 + 1.28185i
\(711\) −11.2112 + 3.29192i −0.420454 + 0.123456i
\(712\) −12.2386 −0.458662
\(713\) −0.817036 0.0552115i −0.0305982 0.00206769i
\(714\) 13.7107 0.513110
\(715\) 27.3081 8.01837i 1.02126 0.299870i
\(716\) −7.33448 8.46445i −0.274103 0.316331i
\(717\) 2.05543 1.32094i 0.0767614 0.0493316i
\(718\) −1.92950 13.4199i −0.0720082 0.500828i
\(719\) 17.3887 + 11.1751i 0.648490 + 0.416759i 0.823114 0.567876i \(-0.192235\pi\)
−0.174624 + 0.984635i \(0.555871\pi\)
\(720\) 1.58816 3.47758i 0.0591871 0.129602i
\(721\) −6.99820 + 8.07636i −0.260627 + 0.300779i
\(722\) 2.04716 14.2383i 0.0761873 0.529894i
\(723\) −4.51289 9.88185i −0.167836 0.367510i
\(724\) −8.43843 2.47775i −0.313612 0.0920847i
\(725\) 5.42890 + 1.59407i 0.201624 + 0.0592022i
\(726\) 3.53167 + 7.73329i 0.131073 + 0.287009i
\(727\) 4.48938 31.2244i 0.166502 1.15805i −0.719543 0.694448i \(-0.755649\pi\)
0.886045 0.463599i \(-0.153442\pi\)
\(728\) −8.92555 + 10.3006i −0.330803 + 0.381767i
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) −42.4969 27.3111i −1.57288 1.01083i
\(731\) 8.27187 + 57.5321i 0.305946 + 2.12790i
\(732\) 10.6456 6.84152i 0.393473 0.252870i
\(733\) 15.9963 + 18.4607i 0.590836 + 0.681861i 0.969898 0.243510i \(-0.0782988\pi\)
−0.379062 + 0.925371i \(0.623753\pi\)
\(734\) −15.6143 + 4.58476i −0.576333 + 0.169227i
\(735\) −5.25527 −0.193843
\(736\) −4.20014 + 2.31491i −0.154819 + 0.0853287i
\(737\) −9.28801 −0.342128
\(738\) 9.97609 2.92924i 0.367225 0.107827i
\(739\) 27.6042 + 31.8570i 1.01544 + 1.17188i 0.985038 + 0.172340i \(0.0551326\pi\)
0.0304000 + 0.999538i \(0.490322\pi\)
\(740\) 15.4981 9.96001i 0.569721 0.366137i
\(741\) 1.43997 + 10.0152i 0.0528986 + 0.367918i
\(742\) −25.0943 16.1271i −0.921240 0.592045i
\(743\) 1.24173 2.71901i 0.0455546 0.0997507i −0.885486 0.464665i \(-0.846175\pi\)
0.931041 + 0.364915i \(0.118902\pi\)
\(744\) 0.111819 0.129046i 0.00409948 0.00473106i
\(745\) −10.0606 + 69.9729i −0.368592 + 2.56361i
\(746\) 2.89747 + 6.34458i 0.106084 + 0.232292i
\(747\) 0.108660 + 0.0319056i 0.00397568 + 0.00116736i
\(748\) −7.18544 2.10983i −0.262726 0.0771432i
\(749\) 12.9431 + 28.3414i 0.472930 + 1.03557i
\(750\) 2.51134 17.4668i 0.0917013 0.637796i
\(751\) −25.6872 + 29.6446i −0.937338 + 1.08175i 0.0591703 + 0.998248i \(0.481155\pi\)
−0.996508 + 0.0834975i \(0.973391\pi\)
\(752\) 2.26617 4.96223i 0.0826388 0.180954i
\(753\) 12.0477 + 7.74258i 0.439042 + 0.282155i
\(754\) 0.394402 + 2.74313i 0.0143633 + 0.0998988i
\(755\) −3.19007 + 2.05013i −0.116099 + 0.0746120i
\(756\) 1.89510 + 2.18706i 0.0689240 + 0.0795426i
\(757\) 45.5285 13.3684i 1.65476 0.485882i 0.684718 0.728808i \(-0.259926\pi\)
0.970045 + 0.242926i \(0.0781074\pi\)
\(758\) 16.5116 0.599728
\(759\) −3.60680 + 6.66747i −0.130918 + 0.242014i
\(760\) 8.21316 0.297923
\(761\) 29.5001 8.66200i 1.06938 0.313997i 0.300755 0.953701i \(-0.402761\pi\)
0.768621 + 0.639704i \(0.220943\pi\)
\(762\) −4.96881 5.73431i −0.180001 0.207732i
\(763\) −20.2394 + 13.0071i −0.732715 + 0.470887i
\(764\) 0.901138 + 6.26755i 0.0326020 + 0.226752i
\(765\) −15.2375 9.79257i −0.550914 0.354051i
\(766\) −9.30027 + 20.3647i −0.336032 + 0.735808i
\(767\) 5.86852 6.77263i 0.211900 0.244546i
\(768\) 0.142315 0.989821i 0.00513534 0.0357171i
\(769\) −13.4905 29.5400i −0.486479 1.06524i −0.980631 0.195864i \(-0.937249\pi\)
0.494153 0.869375i \(-0.335478\pi\)
\(770\) 16.7792 + 4.92680i 0.604679 + 0.177550i
\(771\) −4.07237 1.19576i −0.146663 0.0430641i
\(772\) −1.27692 2.79607i −0.0459575 0.100633i
\(773\) −1.76947 + 12.3070i −0.0636435 + 0.442650i 0.932938 + 0.360037i \(0.117236\pi\)
−0.996582 + 0.0826137i \(0.973673\pi\)
\(774\) −8.03389 + 9.27160i −0.288772 + 0.333261i
\(775\) 0.682077 1.49354i 0.0245009 0.0536495i
\(776\) 0.734866 + 0.472270i 0.0263802 + 0.0169535i
\(777\) 1.98460 + 13.8032i 0.0711971 + 0.495187i
\(778\) −6.34496 + 4.07766i −0.227478 + 0.146191i
\(779\) 14.6274 + 16.8809i 0.524081 + 0.604821i
\(780\) 17.2765 5.07284i 0.618599 0.181637i
\(781\) 18.6858 0.668629
\(782\) 8.02396 + 21.2577i 0.286936 + 0.760175i
\(783\) 0.588417 0.0210283
\(784\) −1.31894 + 0.387276i −0.0471051 + 0.0138313i
\(785\) −20.3033 23.4312i −0.724654 0.836296i
\(786\) −14.9815 + 9.62803i −0.534372 + 0.343420i
\(787\) 0.584258 + 4.06361i 0.0208266 + 0.144852i 0.997581 0.0695074i \(-0.0221428\pi\)
−0.976755 + 0.214359i \(0.931234\pi\)
\(788\) −0.810476 0.520862i −0.0288720 0.0185549i
\(789\) 2.95101 6.46180i 0.105059 0.230046i
\(790\) −29.2531 + 33.7598i −1.04078 + 1.20112i
\(791\) −3.09410 + 21.5199i −0.110013 + 0.765160i
\(792\) −0.656624 1.43781i −0.0233321 0.0510902i
\(793\) 57.1859 + 16.7913i 2.03073 + 0.596277i
\(794\) −27.5932 8.10211i −0.979248 0.287533i
\(795\) 16.3704 + 35.8461i 0.580597 + 1.27133i
\(796\) −0.465837 + 3.23997i −0.0165111 + 0.114838i
\(797\) 25.2895 29.1857i 0.895801 1.03381i −0.103432 0.994637i \(-0.532982\pi\)
0.999232 0.0391727i \(-0.0124722\pi\)
\(798\) −2.58264 + 5.65520i −0.0914246 + 0.200192i
\(799\) −21.7428 13.9732i −0.769203 0.494337i
\(800\) −1.36847 9.51790i −0.0483826 0.336509i
\(801\) −10.2958 + 6.61670i −0.363784 + 0.233790i
\(802\) −4.46331 5.15093i −0.157605 0.181886i
\(803\) −20.0399 + 5.88425i −0.707193 + 0.207651i
\(804\) −5.87608 −0.207233
\(805\) −18.7372 49.6402i −0.660401 1.74959i
\(806\) 0.804211 0.0283271
\(807\) −7.41913 + 2.17845i −0.261166 + 0.0766852i
\(808\) 7.14472 + 8.24544i 0.251350 + 0.290074i
\(809\) 30.9861 19.9136i 1.08941 0.700123i 0.132700 0.991156i \(-0.457635\pi\)
0.956713 + 0.291033i \(0.0939989\pi\)
\(810\) −0.544078 3.78415i −0.0191170 0.132961i
\(811\) −37.6052 24.1674i −1.32050 0.848631i −0.325212 0.945641i \(-0.605436\pi\)
−0.995283 + 0.0970099i \(0.969072\pi\)
\(812\) −0.707376 + 1.54894i −0.0248240 + 0.0543571i
\(813\) −3.32707 + 3.83965i −0.116686 + 0.134662i
\(814\) 1.08399 7.53931i 0.0379938 0.264253i
\(815\) −36.6482 80.2484i −1.28373 2.81098i
\(816\) −4.54589 1.33479i −0.159138 0.0467271i
\(817\) −25.2882 7.42529i −0.884722 0.259778i
\(818\) −11.5463 25.2829i −0.403708 0.883996i
\(819\) −1.93971 + 13.4910i −0.0677789 + 0.471412i
\(820\) 26.0302 30.0405i 0.909016 1.04906i
\(821\) 15.4538 33.8391i 0.539341 1.18099i −0.422244 0.906482i \(-0.638757\pi\)
0.961584 0.274509i \(-0.0885154\pi\)
\(822\) 0.641849 + 0.412491i 0.0223871 + 0.0143873i
\(823\) −5.84078 40.6235i −0.203597 1.41605i −0.793498 0.608572i \(-0.791743\pi\)
0.589902 0.807475i \(-0.299167\pi\)
\(824\) 3.10657 1.99647i 0.108223 0.0695505i
\(825\) −9.95332 11.4867i −0.346530 0.399917i
\(826\) 5.28324 1.55130i 0.183827 0.0539766i
\(827\) 6.42848 0.223540 0.111770 0.993734i \(-0.464348\pi\)
0.111770 + 0.993734i \(0.464348\pi\)
\(828\) −2.28185 + 4.21819i −0.0792998 + 0.146592i
\(829\) 15.8721 0.551262 0.275631 0.961264i \(-0.411113\pi\)
0.275631 + 0.961264i \(0.411113\pi\)
\(830\) 0.415415 0.121977i 0.0144193 0.00423388i
\(831\) −10.0789 11.6317i −0.349634 0.403499i
\(832\) 3.96215 2.54632i 0.137363 0.0882776i
\(833\) 0.926852 + 6.44640i 0.0321135 + 0.223355i
\(834\) −7.76151 4.98802i −0.268759 0.172721i
\(835\) −8.39313 + 18.3784i −0.290456 + 0.636010i
\(836\) 2.22374 2.56633i 0.0769095 0.0887583i
\(837\) 0.0243006 0.169014i 0.000839951 0.00584199i
\(838\) −6.29007 13.7733i −0.217287 0.475792i
\(839\) −10.0042 2.93748i −0.345382 0.101413i 0.104441 0.994531i \(-0.466695\pi\)
−0.449823 + 0.893118i \(0.648513\pi\)
\(840\) 10.6154 + 3.11696i 0.366265 + 0.107545i
\(841\) −11.9032 26.0644i −0.410455 0.898772i
\(842\) −5.42852 + 37.7562i −0.187079 + 1.30117i
\(843\) −2.16076 + 2.49365i −0.0744206 + 0.0858860i
\(844\) −10.1434 + 22.2109i −0.349149 + 0.764530i
\(845\) 29.5318 + 18.9789i 1.01593 + 0.652896i
\(846\) −0.776356 5.39968i −0.0266917 0.185645i
\(847\) −20.6970 + 13.3012i −0.711158 + 0.457034i
\(848\) 6.75016 + 7.79010i 0.231801 + 0.267513i
\(849\) −24.8342 + 7.29197i −0.852307 + 0.250260i
\(850\) −45.5576 −1.56261
\(851\) −20.2397 + 11.1551i −0.693808 + 0.382392i
\(852\) 11.8216 0.405001
\(853\) −25.2284 + 7.40772i −0.863803 + 0.253636i −0.683478 0.729971i \(-0.739533\pi\)
−0.180326 + 0.983607i \(0.557715\pi\)
\(854\) 23.9815 + 27.6761i 0.820628 + 0.947056i
\(855\) 6.90935 4.44037i 0.236295 0.151858i
\(856\) −1.53223 10.6569i −0.0523704 0.364244i
\(857\) 27.2849 + 17.5349i 0.932033 + 0.598981i 0.916125 0.400892i \(-0.131300\pi\)
0.0159081 + 0.999873i \(0.494936\pi\)
\(858\) 3.09258 6.77180i 0.105579 0.231185i
\(859\) 36.1249 41.6904i 1.23257 1.42246i 0.360724 0.932673i \(-0.382530\pi\)
0.871843 0.489785i \(-0.162925\pi\)
\(860\) −6.67479 + 46.4242i −0.227609 + 1.58305i
\(861\) 12.4992 + 27.3695i 0.425973 + 0.932750i
\(862\) −9.80006 2.87756i −0.333791 0.0980100i
\(863\) −17.4765 5.13157i −0.594908 0.174681i −0.0296015 0.999562i \(-0.509424\pi\)
−0.565306 + 0.824881i \(0.691242\pi\)
\(864\) −0.415415 0.909632i −0.0141327 0.0309463i
\(865\) −7.82961 + 54.4562i −0.266215 + 1.85156i
\(866\) 6.43251 7.42351i 0.218585 0.252261i
\(867\) −2.26266 + 4.95453i −0.0768440 + 0.168265i
\(868\) 0.415696 + 0.267152i 0.0141097 + 0.00906773i
\(869\) 2.62843 + 18.2811i 0.0891634 + 0.620145i
\(870\) 1.89245 1.21620i 0.0641599 0.0412331i
\(871\) −18.1234 20.9156i −0.614089 0.708696i
\(872\) 7.97681 2.34220i 0.270129 0.0793170i
\(873\) 0.873537 0.0295648
\(874\) −10.2796 0.694644i −0.347711 0.0234967i
\(875\) 51.0668 1.72637
\(876\) −12.6783 + 3.72268i −0.428360 + 0.125778i
\(877\) 18.8581 + 21.7634i 0.636791 + 0.734896i 0.978804 0.204799i \(-0.0656541\pi\)
−0.342013 + 0.939695i \(0.611109\pi\)
\(878\) −6.55842 + 4.21484i −0.221336 + 0.142244i
\(879\) 0.928701 + 6.45925i 0.0313243 + 0.217865i
\(880\) −5.08361 3.26704i −0.171369 0.110132i
\(881\) −8.74991 + 19.1596i −0.294792 + 0.645505i −0.997844 0.0656341i \(-0.979093\pi\)
0.703052 + 0.711139i \(0.251820\pi\)
\(882\) −0.900187 + 1.03887i −0.0303109 + 0.0349806i
\(883\) 2.01508 14.0152i 0.0678127 0.471648i −0.927412 0.374041i \(-0.877972\pi\)
0.995225 0.0976071i \(-0.0311188\pi\)
\(884\) −9.26963 20.2977i −0.311771 0.682684i
\(885\) −6.97957 2.04939i −0.234616 0.0688894i
\(886\) 27.0777 + 7.95073i 0.909693 + 0.267110i
\(887\) 23.8989 + 52.3313i 0.802446 + 1.75711i 0.636954 + 0.770901i \(0.280194\pi\)
0.165492 + 0.986211i \(0.447079\pi\)
\(888\) 0.685789 4.76977i 0.0230136 0.160063i
\(889\) 14.3792 16.5945i 0.482263 0.556561i
\(890\) −19.4369 + 42.5608i −0.651525 + 1.42664i
\(891\) −1.32972 0.854562i −0.0445474 0.0286289i
\(892\) −2.16306 15.0444i −0.0724246 0.503724i
\(893\) 9.85910 6.33606i 0.329922 0.212028i
\(894\) 12.1091 + 13.9746i 0.404988 + 0.467381i
\(895\) −41.0841 + 12.0634i −1.37329 + 0.403234i
\(896\) 2.89389 0.0966782
\(897\) −22.0522 + 4.88795i −0.736303 + 0.163204i
\(898\) −12.7574 −0.425721
\(899\) 0.0964038 0.0283067i 0.00321525 0.000944081i
\(900\) −6.29699 7.26712i −0.209900 0.242237i
\(901\) 41.0836 26.4028i 1.36869 0.879606i
\(902\) −2.33885 16.2671i −0.0778753 0.541635i
\(903\) −29.8666 19.1941i −0.993899 0.638740i
\(904\) 3.12092 6.83387i 0.103800 0.227291i
\(905\) −22.0181 + 25.4102i −0.731906 + 0.844665i
\(906\) −0.141160 + 0.981791i −0.00468974 + 0.0326178i
\(907\) 18.7643 + 41.0880i 0.623057 + 1.36430i 0.913275 + 0.407344i \(0.133545\pi\)
−0.290218 + 0.956961i \(0.593728\pi\)
\(908\) −12.4086 3.64350i −0.411794 0.120914i
\(909\) 10.4683 + 3.07378i 0.347213 + 0.101951i
\(910\) 21.6461 + 47.3983i 0.717561 + 1.57124i
\(911\) −3.47784 + 24.1889i −0.115226 + 0.801414i 0.847473 + 0.530839i \(0.178123\pi\)
−0.962699 + 0.270576i \(0.912786\pi\)
\(912\) 1.40685 1.62359i 0.0465855 0.0537626i
\(913\) 0.0743612 0.162828i 0.00246100 0.00538883i
\(914\) 7.88287 + 5.06601i 0.260742 + 0.167569i
\(915\) −6.88502 47.8863i −0.227612 1.58307i
\(916\) −0.797930 + 0.512799i −0.0263644 + 0.0169433i
\(917\) −33.7489 38.9483i −1.11449 1.28619i
\(918\) −4.54589 + 1.33479i −0.150037 + 0.0440547i
\(919\) −1.40194 −0.0462457 −0.0231229 0.999733i \(-0.507361\pi\)
−0.0231229 + 0.999733i \(0.507361\pi\)
\(920\) 1.37979 + 18.2828i 0.0454904 + 0.602764i
\(921\) −4.61726 −0.152144
\(922\) 11.1847 3.28413i 0.368349 0.108157i
\(923\) 36.4610 + 42.0783i 1.20013 + 1.38502i
\(924\) 3.84808 2.47301i 0.126593 0.0813561i
\(925\) −6.59439 45.8650i −0.216822 1.50803i
\(926\) 11.4645 + 7.36778i 0.376747 + 0.242120i
\(927\) 1.53404 3.35908i 0.0503845 0.110327i
\(928\) 0.385331 0.444696i 0.0126491 0.0145979i
\(929\) 1.24366 8.64984i 0.0408031 0.283792i −0.959196 0.282741i \(-0.908756\pi\)
0.999999 0.00105110i \(-0.000334576\pi\)
\(930\) −0.271181 0.593804i −0.00889239 0.0194716i
\(931\) −2.83351 0.831994i −0.0928646 0.0272675i
\(932\) −13.3832 3.92967i −0.438382 0.128721i
\(933\) 4.46157 + 9.76947i 0.146065 + 0.319838i
\(934\) −0.936004 + 6.51005i −0.0306270 + 0.213015i
\(935\) −18.7487 + 21.6372i −0.613148 + 0.707611i
\(936\) 1.95653 4.28419i 0.0639511 0.140033i
\(937\) 6.69009 + 4.29946i 0.218556 + 0.140457i 0.645338 0.763897i \(-0.276717\pi\)
−0.426782 + 0.904354i \(0.640353\pi\)
\(938\) −2.42003 16.8317i −0.0790168 0.549574i
\(939\) −22.4530 + 14.4296i −0.732725 + 0.470894i
\(940\) −13.6575 15.7616i −0.445458 0.514086i
\(941\) −19.8857 + 5.83896i −0.648255 + 0.190345i −0.589298 0.807916i \(-0.700596\pi\)
−0.0589567 + 0.998261i \(0.518777\pi\)
\(942\) −8.10972 −0.264229
\(943\) −35.1200 + 35.3970i −1.14367 + 1.15268i
\(944\) −1.90272 −0.0619284
\(945\) 10.6154 3.11696i 0.345318 0.101395i
\(946\) 12.6987 + 14.6551i 0.412871 + 0.476479i
\(947\) 46.2003 29.6911i 1.50131 0.964832i 0.506590 0.862187i \(-0.330906\pi\)
0.994718 0.102645i \(-0.0327306\pi\)
\(948\) 1.66288 + 11.5656i 0.0540079 + 0.375633i
\(949\) −52.3540 33.6458i −1.69948 1.09219i
\(950\) 8.58156 18.7910i 0.278422 0.609660i
\(951\) 12.5611 14.4963i 0.407323 0.470076i
\(952\) 1.95123 13.5711i 0.0632399 0.439843i
\(953\) 3.60974 + 7.90422i 0.116931 + 0.256043i 0.959044 0.283259i \(-0.0914155\pi\)
−0.842113 + 0.539302i \(0.818688\pi\)
\(954\) 9.89024 + 2.90404i 0.320208 + 0.0940217i
\(955\) 23.2270 + 6.82007i 0.751609 + 0.220692i
\(956\) −1.01498 2.22250i −0.0328268 0.0718807i
\(957\) 0.132364 0.920613i 0.00427873 0.0297592i
\(958\) −6.05122 + 6.98348i −0.195506 + 0.225626i
\(959\) −0.917215 + 2.00842i −0.0296184 + 0.0648553i
\(960\) −3.21616 2.06690i −0.103801 0.0667090i
\(961\) 4.40761 + 30.6556i 0.142181 + 0.988890i
\(962\) 19.0928 12.2702i 0.615578 0.395608i
\(963\) −7.05053 8.13674i −0.227200 0.262203i
\(964\) −10.4235 + 3.06062i −0.335719 + 0.0985760i
\(965\) −11.7515 −0.378295
\(966\) −13.0225 4.79898i −0.418993 0.154405i
\(967\) 39.3485 1.26536 0.632681 0.774412i \(-0.281954\pi\)
0.632681 + 0.774412i \(0.281954\pi\)
\(968\) 8.15719 2.39517i 0.262182 0.0769835i
\(969\) −6.66538 7.69226i −0.214123 0.247111i
\(970\) 2.80944 1.80552i 0.0902056 0.0579716i
\(971\) 2.29390 + 15.9545i 0.0736149 + 0.512003i 0.992951 + 0.118529i \(0.0378178\pi\)
−0.919336 + 0.393474i \(0.871273\pi\)
\(972\) −0.841254 0.540641i −0.0269832 0.0173411i
\(973\) 11.0913 24.2866i 0.355572 0.778594i
\(974\) 24.9008 28.7371i 0.797873 0.920795i
\(975\) 6.44522 44.8275i 0.206412 1.43563i
\(976\) −5.25686 11.5109i −0.168268 0.368455i
\(977\) 34.1171 + 10.0177i 1.09150 + 0.320494i 0.777472 0.628918i \(-0.216502\pi\)
0.314032 + 0.949412i \(0.398320\pi\)
\(978\) −22.1412 6.50124i −0.707998 0.207887i
\(979\) 8.03618 + 17.5968i 0.256837 + 0.562395i
\(980\) −0.747902 + 5.20177i −0.0238909 + 0.166165i
\(981\) 5.44423 6.28298i 0.173821 0.200600i
\(982\) −1.78074 + 3.89927i −0.0568255 + 0.124431i
\(983\) −45.9456 29.5274i −1.46544 0.941779i −0.998341 0.0575723i \(-0.981664\pi\)
−0.467096 0.884207i \(-0.654700\pi\)
\(984\) −1.47968 10.2914i −0.0471706 0.328078i
\(985\) −3.09850 + 1.99128i −0.0987264 + 0.0634476i
\(986\) −1.82562 2.10688i −0.0581397 0.0670968i
\(987\) 15.1473 4.44765i 0.482144 0.141570i
\(988\) 10.1182 0.321903
\(989\) 12.2806 57.5397i 0.390499 1.82966i
\(990\) −6.04290 −0.192056
\(991\) −25.7849 + 7.57113i −0.819084 + 0.240505i −0.664321 0.747447i \(-0.731279\pi\)
−0.154762 + 0.987952i \(0.549461\pi\)
\(992\) −0.111819 0.129046i −0.00355026 0.00409722i
\(993\) −7.35311 + 4.72556i −0.233344 + 0.149961i
\(994\) 4.86866 + 33.8623i 0.154424 + 1.07405i
\(995\) 10.5274 + 6.76555i 0.333741 + 0.214482i
\(996\) 0.0470448 0.103014i 0.00149067 0.00326412i
\(997\) 17.6635 20.3847i 0.559408 0.645591i −0.403641 0.914917i \(-0.632256\pi\)
0.963049 + 0.269327i \(0.0868011\pi\)
\(998\) 4.30920 29.9712i 0.136405 0.948721i
\(999\) −2.00181 4.38335i −0.0633344 0.138683i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 138.2.e.b.55.1 10
3.2 odd 2 414.2.i.e.55.1 10
23.8 even 11 3174.2.a.ba.1.5 5
23.15 odd 22 3174.2.a.bb.1.1 5
23.18 even 11 inner 138.2.e.b.133.1 yes 10
69.8 odd 22 9522.2.a.bs.1.1 5
69.38 even 22 9522.2.a.br.1.5 5
69.41 odd 22 414.2.i.e.271.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.2.e.b.55.1 10 1.1 even 1 trivial
138.2.e.b.133.1 yes 10 23.18 even 11 inner
414.2.i.e.55.1 10 3.2 odd 2
414.2.i.e.271.1 10 69.41 odd 22
3174.2.a.ba.1.5 5 23.8 even 11
3174.2.a.bb.1.1 5 23.15 odd 22
9522.2.a.br.1.5 5 69.38 even 22
9522.2.a.bs.1.1 5 69.8 odd 22